None of my business really but since you asked semi-publicly, I'll jump in with my one-fiftieth of a dollar's worth of opinion from my window seat on the rocketsled to Fogeyville.
Trying to duplicate a recipe as an intellectual exercise or a way of saving money is one thing. But trying to knock off a recipe your friend makes for the purpose of presenting it to him as proof that you can do it strikes me as entirely the wrong motivation.
Your friend obviously takes a lot of pride in his signature creation and that's why chooses to keep it a secret. Re-creating his recipe then giving him the final product impresses me as an act of one-upmanship that may be viewed as diminishing the time and effort and esteem he's invested in developing his own special relish.
Viewed another way, you probably have something that you believe you do better than any one else and try to keep that a secret. How would you feel if somebody, just for fun, duplicated what you do and in a sense rubbed your nose in it to celebrate his or her triumph?
My advice - should you decide to continue to experiment with duplicating his recipe - would be to keep any successful results to yourself and graciously appreciate your friend's very personal gift every time he chooses to share some of his relish with you.
Ken